Question: $J$ $K$ $L$ If: $ JL = 81$, $ KL = 6x + 2$, and $ JK = 3x + 7$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {3x + 7} + {6x + 2} = {81}$ Combine like terms: $ 9x + 9 = {81}$ Subtract $9$ from both sides: $ 9x = 72$ Divide both sides by $9$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $KL$ $ KL = 6({8}) + 2$ Simplify: $ {KL = 48 + 2}$ Simplify to find ${KL}$ : $ {KL = 50}$